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摘要
The heat capacity of three synthetic polycrystalline almandine garnets (ideal formula Fe3Al2Si3O12) and one natural almandine-rich single crystal was measured. The samples were characterized by optical microscopy, electron microprobe analysis, X-ray powder diffraction, and Mossbauer spectroscopy. Measurements were performed in the temperature range 3 to 300 K using relaxation calorimetry and between 282 and 764 K using DSC methods. All garnets show a prominent lambda-type heat-capacity anomaly at low temperatures resulting from a paramagnetic-antiferromagnetic phase transition. For two Fe3+-free or nearly Fe3+-free synthetic almandines, the phase transition is sharp and occurs at 9.2 K. Almandine samples that have similar to 3% Fe3+ show a lambda-type peak that is less sharp and that occurs at 8.0 +/- 0.2 K. The low-T C-p data were adjusted slightly using the DSC results to improve the experimental accuracy. Integration of the low-T C-p data yields calorimetric standard entropy, S degrees, values between 336.7 +/- 0.8 and 337.8 +/- 0.8 J/(mol.K). The smaller value is recommended as the best S degrees for end-member stoichiometric almandine, because it derives from the %26quot;best%26quot; Fe3+-free synthetic sample. %26lt;br%26gt;The lattice (vibrational) heat capacity of almandine was calculated using the single-parameter phonon dispersion model of Komada and Westrum (1997), which allows the non-lattice heat capacity (C-ex) behavior to be modeled. An analysis shows the presence of an electronic heat-capacity contribution (C-el, Schottky anomaly) superimposed on a larger magnetic heat-capacity effect (C-mag) around 17 K. The calculated lattice entropy at 298.15 K is S-vib = 303.3 J/(mol.K) and it contributes about 90% to the total standard entropy at 298 K. The non-lattice entropy is S-ex = 33.4 J/(mol.K) and consists of S-mag = 32.1 J/(mol.K) and S-el = 1.3 J/(mol.K) contributions. The C-p behavior for almandine above 298 K is given by the polynomial [in J/(mol.K)]: %26lt;br%26gt;C-p = 649.06(+/- 4) - 3837.57(+/- 122).T-0.5-1.44682(+/- 0.06).10(7).T-2 + 1.94834(+/- 0.09).10(9).T-3 %26lt;br%26gt;which is calculated using the measured DSC data together with one published heat-content datum determined by transposed-drop calorimetry along with a new determination in this work that gives H-1181K - H-302K = 415.0 +/- 3.2 kJ/mol. %26lt;br%26gt;Using our S degrees value and the C-p polynomial for almandine, we derived the enthalpy of formation, Delta H-f(o), from an analysis of experimental phase equilibrium results on the reactions almandine + 3rutile = 3ilmenite + sillimanite + 2quartz and 2ilmenite = 2Fe + 2rutile + O-2. A Delta H-f(o) = -5269.63 kJ/mol was obtained.
- 出版日期2012-10
